STA3045S - Advanced Stochastic Processes & Distribution

Course Outline:

This course is a third-year module for students studying Actuarial Science or Mathematical Statistics, though not a requirement for a major in Mathematical Statistics. The course begins by giving a brief introduction to copulas and extreme value theory, together with some applications to risk management. The rest of the course gives a theoretical overview of stochastic processes, with the models covered spanning both discrete and continuous time as well as discrete and continuous state-space. Though the emphasis is on the theoretical properties of the models, the application of the methods to real-world problems is also explored at length. Topics covered: copulas, an introduction to extreme value theory, homogenous and non-homogeneous continuous-time Markov chains, random walks, probability theory, martingales, Brownian motion, and diffusion processes.